This paper is concerned with a study of approximation order and construction of locally supported elements for the space S41 (Δ) of Cl quartic pp (piecewise polynomial) functions on a triangulation Δ of a connected polygonal domain Ω in R2. It is well known that, when Δ is a three-directional mesh Δ(1), the order of approximation of S41(Δ(1)) is only 4, not 5. Though a local Clough-Tocher refinement procedure of an arbitrary triangulation A yields the optimal (fifth) order of approximation from the space S41(Δ) (see [1]), it needs more data points in addition to the vertex set of the triangulation A. In this paper, we will introduce a particular mixed three-directional mesh Δ(3)) and construct so-called mixed three-directional elements. We prove that the space S41(Δ(3)) achieves its optimal-order of approximation by constructing an interpolation scheme using mixed three-directional elements.

Understanding police use of lethal force requires the collection of reliable data. Due to bias present in police-use-of-lethal-force databases, researchers typically triangulate using multiple data sources to compensate for this bias; however, triangulation is restricted when the bias present in each database is unknown. This study investigates three government-funded and three independent police-use-of-lethal-force databases to identify methodological sources of bias present in the major U.S. data-collection systems. Bias was coded based on nine categories, including misclassification bias, broad conceptualization, narrow conceptualization, overlap bias, coverage bias, voluntary response bias, observer bias, gatekeeping bias, and self-report response bias. Findings suggest that all six databases had at least three different types of methodological bias present. Generally, public, government-sponsored databases exhibit bias through data self-reporting by law enforcement and varying victim race determination methods. Private databases reveal bias through media-based reporting and the triangulation of data from multiple sources, which is further complicated by lack of transparency in the databases' design and administrative procedures. All six databases have a unique position to the State, which should also inform researcher data selection. I argue that selecting data sources that complement each other based on these identified biases will produce a more complete image of police-use-of-lethal-force and enhance finding accuracy in future research. / Master of Science / Understanding incidents where a civilian dies due to the actions of police officers requires the collection of reliable data. Due to bias—flaws in the data collection methods or data presentation—which lead to varying results when using different databases, researchers typically use multiple data sources to make up for these flaws; however, this method is restricted when the bias present in each database is unknown. This study investigates three government-funded and three independent police-use-of-lethal-force databases to identify sources of bias present in the major U.S. data-collection systems. Findings suggest that all six databases had at least three different types of flaws present. Generally, public, government-sponsored databases exhibit bias through police self-reporting lethal force, where an officer's department reports the officer's actions and there is no individual or group outside of the police reporting these incidents. Additionally, there is a flaw in how police record the race of a victim, who dies through police use of lethal force; Varying procedures in how race is recorded, whether recorded based on the officer's opinion or where a victim self-reports their own race prior to death on a government data system such as the Department of Motor Vehicles, also impacts the race data included in public databases. Private databases reveal bias through collecting incident data from news reports and using data from multiple sources such as law enforcement reports, medical examiner reports, and media reports simultaneously; this is further complicated by lack of transparency in the databases' design and administrative procedures, where there are no documents detailing the steps databases take in collecting and presenting data. All six databases have a unique position to the U.S. Government, where some are funded by the Government and where some are motivated by recent high profile police killings, which should impact researcher data selection. Ideally, the databases used should hold multiple perspectives or positions to the Government to provide an more complete image of lethal force. I argue that selecting data sources that complement each other based on these identified biases will produce a more complete image of police-use-of-lethal-force and enhance finding accuracy in future research.

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This thesis describes an investigation into the experimental accuracy of a close-up stereo vision system. Surfaces are measured from any orientation through the synergy of a Coordinate Measurement Machine (CMM) and a custom made stereo vision head. Calibration of the stereo cameras is achieved using bundle adjustment non-linear optimization, commonly used in photogrammetry. Point set registration techniques are used to calibrate the stereo head with respect to the CMM coordinate system. The fully calibrated stereo vision system is used to provide experimental accuracy results under ideal imagining conditions. The system is then applied to the practical problem of sheet metal strain analysis. This problem involves many non-ideal imaging components that affect system accuracy. Experimental results for this non-deal situation are provided in the form of three-dimensional strain distribution plots. / Thesis / Master of Engineering (ME)

Dress is both an individual and a societal means of communication. Understanding the meaning of dress within a society, culture, and specific time period can aid researchers in understanding the social, political, and economic events and changes that take place in dress. The Scottish Highland dress differed in the 17th and early 18th centuries from that of the Scottish Lowlanders (i.e., people of Scotland below the Highlands) due to differences in culture and geography. Highland dress has been difficult to study because few extant garments exist before the 19th century and most of the records that exist deal with the upper class garments. The purpose of this research was to determine whether or not poetry (i.e., poems, ballads, and songs) could be used as a source of knowledge on historic dress in a social, political, or economic context, using the dress of Scottish Highlanders from 1603 through 1830 as an example, and to triangulate the findings with other sources that portray dress through the written word or visual image. This research cross-referenced the items of dress with social, political, and economic events that occurred in the lives of the Scottish and Highland people. The main source of documentation for this research was 3,501 Scottish poems written between 1603 and 1830 gathered from 18 anthologies and there were 394 poems with male dress references and 245 poems with female dress references, which was 18% of the poems. A large number (N=1531) of individual dress items were referenced within those poems. The poems were triangulated with 34 letters and 332 portraits from the same time period. The study of Highland dress in poetry expanded the knowledge base regarding specific items worn by males and females. The majority of the poems and dress references were found in the 18th century. The plaid and the kilt were the focus of poems related to war. The letters and portraits provided new information on dress, as well as providing support for the information gathered in the poems. Triangulation with the letters and portraits validated poetry as a source of Highland dress between 1603 and 1830. / Ph. D.